A current I flows an infinitely long wire with cross section in the form of a semi-circular ring of radius R. The magnitude of the magnetic induction along its axis is :

Engineering

Physics

Magnetic Field

Question

$\frac{μ_{0} I}{4 πR}$

$\frac{μ_{0} I}{2 πR}$

$\frac{μ_{0} I}{2 π^{2} R}$

$\frac{μ_{0} I}{π^{2} R}$

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$v = \frac{I}{πR}$

$dB = (\frac{μ_{0}}{4 π}) \frac{2 I}{R}$ I = λR dθ

∴ $B = \int_{- π / 2}^{π / 2} dBcosθ$

$= \frac{μ_{0} λ}{2 π} \int_{- π / 2}^{π / 2} cosθdθ$

$= \frac{μ_{0} λ}{π} = \frac{μ_{0} I}{π^{2} R}$